Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 63


$V(x)= 4x^{3}-64x^{2}+240x$

Work Step by Step

From the figure, we can see that the box will have a length $20 - 2x$ in, a width $12 - 2x$ and a height $x$. The volume of a rectangular box is found by multiplying its length by its width by its height. Therefore, the volume $V$ of the box as a function of $x$ will be: $V(x) = (20 - 2x)(12 - 2x)x$ Simplifying, we get: $V(x) = (20 - 2x)(12 - 2x)x$ $= x(240 - 40x-24x+4x^{2})$ $= x(4x^{2}-64x+240)$ $= 4x^{3}-64x^{2}+240x$
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